@Article{cmes.2010.058.271,
AUTHOR = {A.  Frangi, M.  Bonnet},
TITLE = {On the application of the Fast Multipole Method to Helmholtz-like problems with complex wavenumber},
JOURNAL = {Computer Modeling in Engineering \& Sciences},
VOLUME = {58},
YEAR = {2010},
NUMBER = {3},
PAGES = {271--296},
URL = {http://www.techscience.com/CMES/v58n3/25492},
ISSN = {1526-1506},
ABSTRACT = {This paper presents an empirical study of the accuracy of multipole expansions of Helmholtz-like kernels with complex wavenumbers of the form k = (α + iβ)ϑ, with α = 0,±1 and β > 0,  which, the paucity of available studies notwithstanding, arise for a wealth of different physical problems. It is suggested that a simple point-wise error indicator can provide an a-priori indication on the number <i>N</i> of terms to be employed in the Gegenbauer addition formula in order to achieve a prescribed accuracy when integrating single layer potentials over surfaces. For β ≥ 1 it is observed that the value of <i>N</i> is independent of β and of the size of the octree cells employed while, for β < 1, simple empirical formulas are proposed yielding the required <i>N</i> in terms of β.},
DOI = {10.3970/cmes.2010.058.271}
}